Past exam of the year 1 of the computer science course of the University of Oxford / 2015 / Discrete mathematics, continuous mathematics, and probability / 3 / c / i

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- Solution i

Solution

The greatest common divisor is the largest positive integer dividing both inputs:

g cd (a, b) = max {d \in N_{+} : d ∣ a and d ∣ b} .

This maximum exists because

1

belongs to the set and all its elements are at most

b

.

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